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No Risk Double Up

Introduction

I first played No Risk Double Up on the day it premiered, Feb. 1, 2013, at the Red Rock. It is one of various games available on the WMS My Poker machines. The thrust of the game is that sometimes on a winning hand the player plays a bonus game in which the player may double his win up to four times, or to a multiplier of 24=16. There is "no risk," because the worst that can happen in the bonus is the player gets paid the base amount for his hand. However, the player pays for the bonus feature via a non-refundable fee equal to his video poker wager.

Rules

Player makes a 10-coin bet. Five coins pay for the standard video poker hand and five enable the No Risk Double Up feature.

The player plays his hand according to standard video poker rules.

If the player gets any paying hand on the draw, then he will have a specified chance of playing the Double Up feature.

This probability depends on the poker hand.

In the Double Up feature, the player will first pick one of five face-down cards. Four are aces and one is a joker, and the goal is to pick an ace. If the player picks the joker, then his multiplier is 1x. Otherwise, see rule 6.

In the next stage, there are three aces and two jokers. If the player picks a joker, his multiplier is 2x. Otherwise, see rule 7.

In the next stage, there are two aces and three jokers. If the player picks the joker, then his multiplier is 4x. Otherwise see rule 8.

In the next stage, there is one ace and four jokers. If the player picks a joker, then his multiplier is 8x. If the player picks the ace, his multiplier is 16x.

Player is paid according to his poker hand and any multiplier earned.

Here is an example, in pictures, of the bonus game.

First I got a four of a kind on the draw. The probability of the bonus feature with a four of a kind is 100%, as seen in the table to the right of the pay table.

Then I was given five cards and challenged to pick one of the four aces.

It isn't clear which card I chose from the picture, but I did pick one of the aces.

Next, I was asked to picked one of three aces in the next set of five cards.

I must have picked one of the jokers, which ended the bonus, giving me a multiplier of 2x.

Odds

The following tables show the probability and return for the pay tables I noticed at the Red Rock. The "bonus prob." column refers to the probability of playing the bonus feature with that hand. The "adjusted pay" column refers to the average win for that hand, considering the probability of playing the bonus and the average bonus multiplier.

55-9-5 Jacks or Better

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

50,841,598

0.000031

0.046954

Straight flush

55

1.000000

105.47

214,210,910

0.000129

0.013601

Four of a kind

25

1.000000

47.94

3,914,082,611

0.002356

0.112962

Full house

9

1.000000

17.26

19,051,457,919

0.011469

0.197939

Flush

5

0.333333

4.86

19,370,987,397

0.011662

0.056706

Straight

4

0.333333

3.89

20,771,970,996

0.012505

0.048646

Three of a kind

3

0.200000

2.35

122,823,581,699

0.073941

0.173803

Two pair

2

0.166667

1.47

212,898,461,571

0.128167

0.188730

Jacks or better

1

0.166667

0.74

334,272,435,996

0.201235

0.148163

Loser

0

0.000000

0.00

927,734,512,403

0.558505

0.000000

Total

1,661,102,543,100

1.000000

0.987504

55-7-5 Jacks or Better

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

50,824,583

0.000031

0.046938

Straight flush

55

1.000000

105.47

214,585,611

0.000129

0.013625

Four of a kind

25

1.000000

47.94

3,892,982,511

0.002344

0.112353

Full house

7

1.000000

13.42

18,929,401,539

0.011396

0.152967

Flush

5

0.500000

6.04

24,123,066,721

0.014522

0.087773

Straight

4

0.250000

3.42

17,575,843,366

0.010581

0.036161

Three of a kind

3

0.200000

2.35

121,993,405,530

0.073441

0.172628

Two pair

2

0.200000

1.57

211,800,539,664

0.127506

0.199807

Jacks or better

1

0.166667

0.74

321,989,453,811

0.193841

0.142719

Loser

0

0.000000

0.00

940,532,439,764

0.566210

0.000000

Total

1,661,102,543,100

1.000000

0.964970

55-7-5 Bonus Poker

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

50,833,965

0.000031

0.046947

Straight flush

55

1.000000

105.47

210,409,105

0.000127

0.013359

Four aces

80

1.000000

153.41

344,139,578

0.000207

0.031782

Four 2-4

40

1.000000

76.70

875,353,709

0.000527

0.040421

Four 5-K

25

1.000000

47.94

2,685,202,897

0.001617

0.077496

Full house

7

0.500000

8.46

18,770,201,496

0.011300

0.095615

Flush

5

0.500000

6.04

22,907,520,905

0.013791

0.083350

Straight

4

0.333333

3.89

19,616,676,850

0.011809

0.045940

Three of a kind

3

0.250000

2.56

122,108,491,916

0.073511

0.188422

Two pair

2

0.250000

1.71

211,395,173,364

0.127262

0.217465

Jacks or better

1

0.166667

0.74

321,751,591,491

0.193698

0.142613

Loser

0

0.000000

0.00

940,386,947,824

0.566122

0.000000

Total

0.000000

1,661,102,543,100

1.000000

0.983411

55-8-5 Bonus Poker

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

51,279,913

0.000031

0.047359

Straight flush

55

1.000000

105.47

204,623,113

0.000123

0.012992

Four aces

80

1.000000

153.41

339,803,845

0.000205

0.031382

Four 2-4

40

1.000000

76.70

887,030,961

0.000534

0.040960

Four 5-K

25

1.000000

47.94

2,706,328,195

0.001629

0.078106

Full house

8

0.500000

9.67

19,146,735,969

0.011527

0.111466

Flush

5

0.250000

4.27

18,359,113,789

0.011052

0.047216

Straight

4

0.250000

3.42

17,807,967,546

0.010721

0.036639

Three of a kind

3

0.250000

2.56

124,025,547,128

0.074665

0.191380

Two pair

2

0.250000

1.71

215,245,052,118

0.129580

0.221426

Jacks or better

1

0.250000

0.85

341,447,589,567

0.205555

0.175626

Loser

0

0.000000

0.00

920,881,470,956

0.554380

0.000000

Total

1,661,102,543,100

1.000000

0.994551

80-9-6 Double Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

50,848,370

0.000031

0.046960

Straight flush

80

1.000000

153.41

232,091,773

0.000140

0.021434

Four aces

160

1.000000

306.82

381,850,707

0.000230

0.070530

Four 2-4

80

1.000000

153.41

899,534,501

0.000542

0.083075

Four 5-K

50

1.000000

95.88

2,684,977,620

0.001616

0.154979

Full house

9

0.250000

7.69

17,359,094,436

0.010450

0.080359

Flush

6

0.250000

5.13

19,625,454,642

0.011815

0.060567

Straight

5

0.200000

3.92

21,636,064,393

0.013025

0.051027

Three of a kind

3

0.200000

2.35

124,196,495,645

0.074768

0.175746

Two pair

1

0.166667

0.74

202,195,087,155

0.121723

0.089621

Jacks or better

1

0.166667

0.74

339,388,020,489

0.204315

0.150430

Loser

0

0.000000

0.00

932,453,023,369

0.561346

0.000000

Total

1.000000

0.984728

55-9-7 Double Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

49,449,663

0.000030

0.045668

Straight flush

55

1.000000

105.47

220,904,899

0.000133

0.014026

Four aces

160

1.000000

306.82

377,831,669

0.000227

0.069788

Four 2-4

80

0.500000

96.70

875,147,954

0.000527

0.050948

Four 5-K

50

0.500000

60.44

2,658,484,847

0.001600

0.096730

Full house

9

0.333333

8.75

17,707,138,842

0.010660

0.093304

Flush

7

0.333333

6.81

24,672,674,798

0.014853

0.101117

Straight

4

0.333333

3.89

20,525,941,554

0.012357

0.048070

Three of a kind

3

0.333333

2.92

122,197,922,340

0.073564

0.214631

Two pair

1

0.200000

0.78

199,755,347,184

0.120255

0.094222

Jacks or better

1

0.200000

0.78

324,521,368,260

0.195365

0.153072

Loser

0

0.000000

0.00

947,540,331,090

0.570429

0.000000

Total

1,661,102,543,100

1.000000

0.981576

55-9-5 Double Double Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

48,363,447

0.000029

0.044665

Straight flush

55

1.000000

105.47

212,523,804

0.000128

0.013494

Four aces + 2-4

400

1.000000

767.04

102,642,886

0.000062

0.047397

Four 2-4 + A-4

160

1.000000

306.82

287,007,958

0.000173

0.053012

Four aces + 5-K

160

1.000000

306.82

289,445,734

0.000174

0.053462

Four 2-4 + 5-K

80

0.500000

96.70

532,887,662

0.000321

0.031023

Four 5-K

50

0.500000

60.44

2,697,263,322

0.001624

0.098141

Full house

9

0.333333

8.75

17,464,609,326

0.010514

0.092026

Flush

5

0.333333

4.86

19,018,885,704

0.011450

0.055675

Straight

4

0.250000

3.42

20,272,323,417

0.012204

0.041709

Three of a kind

3

0.250000

2.56

125,397,768,299

0.075491

0.193498

Two pair

1

0.250000

0.85

203,984,111,961

0.122800

0.104921

Jacks or better

1

0.166667

0.74

345,489,472,116

0.207988

0.153135

Loser

0

0.000000

0.00

925,305,237,464

0.557043

0.000000

Total

0.00

1,661,102,543,100

1.000000

0.982158

55-9-6 Double Double Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

28,668,371

0.000017

0.026476

Straight flush

55

1.000000

105.47

211,274,677

0.000127

0.013414

Four aces + 2-4

400

1.000000

767.04

103,310,572

0.000062

0.047705

Four 2-4 + A-4

160

1.000000

306.82

287,043,734

0.000173

0.053019

Four aces + 5-K

160

1.000000

306.82

288,541,935

0.000174

0.053295

Four 2-4 + 5-K

80

0.500000

96.70

531,884,343

0.000320

0.030965

Four 5-K

50

0.500000

60.44

2,679,069,506

0.001613

0.097479

Full house

9

0.333333

8.75

17,337,699,378

0.010437

0.091357

Flush

6

0.333333

5.84

25,108,867,497

0.015116

0.088204

Straight

4

0.250000

3.42

19,915,596,512

0.011989

0.040975

Three of a kind

3

0.250000

2.56

123,946,114,922

0.074617

0.191258

Two pair

1

0.250000

0.85

201,287,917,422

0.121177

0.103534

Jacks or better

1

0.166667

0.74

330,338,086,155

0.198867

0.146419

Loser

0

0.000000

0.00

939,038,468,076

0.565310

0.000000

Total

1,661,102,543,100

1.000000

0.984100

55-8-5 Double Double Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

48,356,129

0.000029

0.044658

Straight flush

55

1.000000

105.47

212,963,213

0.000128

0.013522

Four aces + 2-4

400

1.000000

767.04

102,638,278

0.000062

0.047395

Four 2-4 + A-4

160

1.000000

306.82

287,016,086

0.000173

0.053014

Four aces + 5-K

160

1.000000

306.82

289,422,478

0.000174

0.053458

Four 2-4 + 5-K

80

0.500000

96.70

532,877,126

0.000321

0.031022

Four 5-K

50

0.500000

60.44

2,695,255,394

0.001623

0.098068

Full house

8

0.333333

7.78

17,457,361,686

0.010510

0.081767

Flush

5

0.333333

4.86

19,023,273,263

0.011452

0.055688

Straight

4

0.250000

3.42

20,353,545,582

0.012253

0.041876

Three of a kind

3

0.250000

2.56

125,317,814,777

0.075443

0.193374

Two pair

1

0.250000

0.85

203,878,772,595

0.122737

0.104867

Jacks or better

1

0.166667

0.74

345,691,511,217

0.208110

0.153224

Loser

0

0.000000

0.00

925,211,735,276

0.556987

0.000000

Total

0.000000

1,661,102,543,100

1.000000

0.971933

55-9-6 Triple Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

47,567,509

0.000029

0.043930

Straight flush

55

1.000000

105.47

229,865,632

0.000138

0.014595

Four aces + 2-4

800

1.000000

1534.08

119,239,081

0.000072

0.110121

Four 2-4 + A-4

400

0.500000

483.52

287,027,419

0.000173

0.083549

Four aces + 5-K

160

0.500000

193.41

231,530,280

0.000139

0.026958

Four 2-4 + 5-K

80

0.333333

77.80

531,240,135

0.000320

0.024882

Four 5-K

50

0.333333

48.63

2,622,157,200

0.001579

0.076760

Full house

9

0.250000

7.69

17,121,315,099

0.010307

0.079258

Flush

6

0.333333

5.84

23,153,412,754

0.013939

0.081334

Straight

4

0.333333

3.89

22,316,795,871

0.013435

0.052264

Three of a kind

2

0.333333

1.95

121,661,348,516

0.073241

0.142459

Two pair

1

0.200000

0.78

198,703,840,446

0.119622

0.093726

Jacks or better

1

0.200000

0.78

331,438,998,621

0.199530

0.156335

Loser

0

0.000000

0.00

942,638,204,537

0.567477

0.000000

Total

1,661,102,543,100

1.000000

0.986172

55-8-5 Triple Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

47,375,452

0.000029

0.043753

Straight flush

55

1.000000

105.47

220,869,185

0.000133

0.014024

Four aces + 2-4

800

1.000000

1534.08

119,312,469

0.000072

0.110189

Four 2-4 + A-4

400

0.500000

483.52

287,533,231

0.000173

0.083696

Four aces + 5-K

160

0.500000

193.41

231,639,169

0.000139

0.026971

Four 2-4 + 5-K

80

0.333333

77.80

532,444,734

0.000321

0.024939

Four 5-K

50

0.333333

48.63

2,658,246,670

0.001600

0.077817

Full house

8

0.333333

7.78

17,284,654,041

0.010406

0.080958

Flush

5

0.333333

4.86

19,735,896,528

0.011881

0.057774

Straight

4

0.333333

3.89

23,603,335,367

0.014209

0.055277

Three of a kind

2

0.333333

1.95

123,207,949,896

0.074172

0.144270

Two pair

1

0.200000

0.78

200,836,822,158

0.120906

0.094732

Jacks or better

1

0.166667

0.74

339,492,887,370

0.204378

0.150477

Loser

0

0.000000

0.00

932,843,576,830

0.561581

0.000000

Total

1,661,102,543,100

1.000000

0.964875

55-8-5 Triple Triple Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal Flush

800

1.000000

1534.08

48,199,494

0.000029

0.044514

Straight Flush

55

1.000000

105.47

233,880,851

0.000141

0.014850

Four Aces with any 2,3,4

800

1.000000

1534.08

119,863,933

0.000072

0.110698

Four 2s, 3s, 4s with an Ace

800

0.500000

967.04

130,893,766

0.000079

0.076202

Four 2s, 3s, 4s with any 2,3,4

400

0.500000

483.52

171,152,540

0.000103

0.049820

Four Aces

160

0.500000

193.41

233,038,056

0.000140

0.027133

Four 2s, 3s, 4s

80

0.333333

77.80

458,450,533

0.000276

0.021473

Four 5s thru Ks

50

0.333333

48.63

2,672,325,558

0.001609

0.078229

Full House

8

0.333333

7.78

17,353,094,178

0.010447

0.081278

Flush

5

0.333333

4.86

19,618,732,075

0.011811

0.057431

Straight

3

0.333333

2.92

17,791,107,475

0.010710

0.031249

Three of a Kind

2

0.250000

1.71

123,642,016,832

0.074434

0.127192

Two Pair

1

0.200000

0.78

205,006,847,508

0.123416

0.096699

Jacks or Better

1

0.200000

0.78

346,069,731,165

0.208337

0.163236

All Other

0

0.000000

0.00

927,553,209,136

0.558396

0.000000

Total

1,661,102,543,100

1.000000

0.980005

55-7-5 Triple Triple Bonus

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal Flush

800

1.000000

1534.08

48,166,386

0.000029

0.044483

Straight Flush

55

1.000000

105.47

234,023,229

0.000141

0.014859

Four Aces with any 2,3,4

800

1.000000

1534.08

119,858,237

0.000072

0.110693

Four 2s, 3s, 4s with an Ace

800

0.500000

967.04

130,780,910

0.000079

0.076136

Four 2s, 3s, 4s with any 2,3,4

400

0.500000

483.52

170,940,298

0.000103

0.049758

Four Aces

160

0.500000

193.41

232,984,197

0.000140

0.027127

Four 2s, 3s, 4s

80

0.333333

77.80

457,438,202

0.000275

0.021425

Four 5s thru Ks

50

0.333333

48.63

2,670,283,660

0.001608

0.078169

Full House

7

0.333333

6.81

17,337,031,320

0.010437

0.071053

Flush

5

0.333333

4.86

19,961,991,360

0.012017

0.058436

Straight

3

0.333333

2.92

17,767,538,673

0.010696

0.031207

Three of a Kind

2

0.250000

1.71

123,484,578,302

0.074339

0.127030

Two Pair

1

0.200000

0.78

204,761,498,130

0.123268

0.096583

Jacks or Better

1

0.200000

0.78

345,329,431,887

0.207892

0.162887

All Other

0

0.000000

0.00

928,395,998,309

0.558903

0.000000

Total

1,661,102,543,100

1.000000

0.969848

"Ugly Ducks" Deuces Wild

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

43,251,497

0.000026

0.039944

Four deuces

200

1.000000

383.52

335,004,142

0.000202

0.077347

Wild royal

25

1.000000

47.94

3,511,011,126

0.002114

0.101329

Five of a kind

15

1.000000

28.76

5,201,941,178

0.003132

0.090078

Straight flush

9

0.500000

10.88

7,391,681,513

0.004450

0.048411

Four of a kind

4

0.250000

3.42

103,169,753,220

0.062109

0.212264

Full house

4

0.200000

3.13

43,687,254,000

0.026300

0.082427

Flush

3

0.200000

2.35

34,526,633,968

0.020785

0.048857

Straight

2

0.200000

1.57

78,437,312,310

0.047220

0.073996

Three of a kind

1

0.200000

0.78

455,582,791,984

0.274265

0.214892

Loser

0

0.000000

0.00

929,215,908,162

0.559397

0.000000

Total

1,661,102,543,100

1.000000

0.989545

16-13 Deuces Wild

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Royal flush

800

1.000000

1534.08

43,496,692

0.000026

0.040171

Four deuces

200

1.000000

383.52

310,326,227

0.000187

0.071649

Wild royal

25

1.000000

47.94

3,428,050,502

0.002064

0.098935

Five of a kind

16

1.000000

30.68

5,062,837,638

0.003048

0.093514

Straight flush

13

0.500000

15.71

9,446,014,693

0.005687

0.089361

Four of a kind

4

0.250000

3.42

100,098,173,079

0.060260

0.205945

Full house

3

0.250000

2.56

42,934,498,656

0.025847

0.066251

Flush

2

0.250000

1.71

31,920,704,349

0.019217

0.032837

Straight

2

0.200000

1.57

88,851,336,959

0.053489

0.083820

Three of a kind

1

0.142857

0.70

443,197,694,512

0.266809

0.187437

Loser

0

0.000000

0.00

935,809,409,793

0.563366

0.000000

Total

1,661,102,543,100

1.000000

0.969920

940-17-7 Joker Wild

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Natural royal flush

940

1.000000

1802.54

55,190,603

0.000027

0.048590

Five of a kind

200

1.000000

383.52

188,141,951

0.000092

0.035243

Wild royal flush

100

1.000000

191.76

232,146,019

0.000113

0.021743

Straight flush

50

1.000000

95.88

1,465,910,588

0.000716

0.068649

Four of a kind

17

0.500000

20.55

17,153,441,573

0.008378

0.172167

Full house

7

0.500000

8.46

31,471,476,975

0.015371

0.130067

Flush

5

0.333333

4.86

37,332,583,750

0.018234

0.088666

Straight

3

0.250000

2.56

34,949,804,574

0.017070

0.043755

Three of a kind

2

0.200000

1.57

267,039,781,532

0.130428

0.204386

Two pair

1

0.166667

0.74

221,701,758,327

0.108284

0.079726

Kings or better

1

0.166667

0.74

259,310,127,713

0.126653

0.093250

Nothing

0

0.000000

0.00

1,176,505,096,495

0.574632

0.000000

Total

2,047,405,460,100

1.000000

0.986242

800-15-7 Joker Wild

Hand

Pays

BonusProb.

AdjustedPay

Combinations

Probability

Return

Natural royal flush

800

1.000000

1534.08

54,663,353

0.000027

0.040958

Five of a kind

200

1.000000

383.52

187,905,361

0.000092

0.035198

Wild royal flush

100

1.000000

191.76

230,670,189

0.000113

0.021605

Straight flush

50

1.000000

95.88

1,473,681,154

0.000720

0.069012

Four of a kind

15

0.500000

18.13

17,119,418,143

0.008362

0.151611

Full house

7

0.500000

8.46

31,411,564,605

0.015342

0.129819

Flush

5

0.333333

4.86

37,565,266,344

0.018348

0.089219

Straight

3

0.200000

2.35

35,011,896,484

0.017101

0.040196

Three of a kind

2

0.200000

1.57

266,400,099,622

0.130116

0.203897

Two pair

1

0.200000

0.78

221,094,494,127

0.107988

0.084610

Kings or better

1

0.200000

0.78

261,766,601,769

0.127853

0.100175

Nothing

0

0.000000

0.00

1,175,089,198,949

0.573941

0.000000

Total

0.000000

0.00

2,047,405,460,100

1.000000

0.966301

The next table shows the Double Up feature probability for some of the above games, assuming optimal strategy.

Feature Probability

Game

Pay Table

FeatureProb.

Jacks or Better

55-9-5

0.091729

Bonus Poker

55-7-5

0.101322

Bonus Poker

55-8-5

0.116178

Double Bonus

80-9-6

0.080023

Double Bonus

55-9-6

0.101723

Double Double Bonus

55-9-5

0.122966

Double Double Bonus

55-9-6

0.096522

Triple Triple Bonus

55-8-5

0.102925

Deuces Wild

25-15-9

0.096939

Joker Wild

940-17-7

0.088410

Finally, for those for whom an average return per hand won't do, here is the 55-9-5 Jacks or Better table broken down by hand and multiplier. This table allows us to see that the standard deviation is 12.09.

55-9-5 Jacks or Better — Detailed Table

Hand

Bonus

Pays

Multiplier

Total win

Total Combinations

Probability

Return

Royal flush

Yes

800

16

6400

73,211,901,120

0.000001

0.007522

Straight flush

Yes

55

16

440

308,463,710,400

0.000005

0.002179

Four of a kind

Yes

25

16

200

5,636,278,959,840

0.000090

0.018097

Full house

Yes

9

16

72

27,434,099,403,360

0.000440

0.031710

Flush

Yes

5

16

40

9,298,073,950,560

0.000149

0.005971

Straight

Yes

4

16

32

9,970,546,078,080

0.000160

0.005122

Three of a kind

Yes

3

16

24

35,373,191,529,312

0.000568

0.013629

Two pair

Yes

2

16

16

51,095,630,777,040

0.000820

0.013124

Jacks or better

Yes

1

16

8

80,225,384,639,040

0.001288

0.010303

Royal flush

Yes

800

8

3200

292,847,604,480

0.000005

0.015044

Straight flush

Yes

55

8

220

1,233,854,841,600

0.000020

0.004358

Four of a kind

Yes

25

8

100

22,545,115,839,360

0.000362

0.036193

Full house

Yes

9

8

36

109,736,397,613,440

0.001762

0.063420

Flush

Yes

5

8

20

37,192,295,802,240

0.000597

0.011941

Straight

Yes

4

8

16

39,882,184,312,320

0.000640

0.010244

Three of a kind

Yes

3

8

12

141,492,766,117,248

0.002271

0.027258

Two pair

Yes

2

8

8

204,382,523,108,160

0.003281

0.026249

Jacks or better

Yes

1

8

4

320,901,538,556,160

0.005152

0.020606

Royal flush

Yes

800

4

1600

549,089,258,400

0.000009

0.014104

Straight flush

Yes

55

4

110

2,313,477,828,000

0.000037

0.004085

Four of a kind

Yes

25

4

50

42,272,092,198,800

0.000679

0.033931

Full house

Yes

9

4

18

205,755,745,525,200

0.003303

0.059456

Flush

Yes

5

4

10

69,735,554,629,200

0.001120

0.011195

Straight

Yes

4

4

8

74,779,095,585,600

0.001200

0.009604

Three of a kind

Yes

3

4

6

265,298,936,469,840

0.004259

0.025554

Two pair

Yes

2

4

4

383,217,230,827,800

0.006152

0.024608

Jacks or better

Yes

1

4

2

601,690,384,792,800

0.009659

0.019319

Royal flush

Yes

800

2

800

610,099,176,000

0.000010

0.007835

Straight flush

Yes

55

2

55

2,570,530,920,000

0.000041

0.002270

Four of a kind

Yes

25

2

25

46,968,991,332,000

0.000754

0.018851

Full house

Yes

9

2

9

228,617,495,028,000

0.003670

0.033031

Flush

Yes

5

2

5

77,483,949,588,000

0.001244

0.006219

Straight

Yes

4

2

4

83,087,883,984,000

0.001334

0.005335

Three of a kind

Yes

3

2

3

294,776,596,077,600

0.004732

0.014197

Two pair

Yes

2

2

2

425,796,923,142,000

0.006836

0.013671

Jacks or better

Yes

1

2

1

668,544,871,992,000

0.010733

0.010733

Royal flush

Yes

800

1

400

381,311,985,000

0.000006

0.002449

Straight flush

Yes

55

1

27.5

1,606,581,825,000

0.000026

0.000709

Four of a kind

Yes

25

1

12.5

29,355,619,582,500

0.000471

0.005891

Full house

Yes

9

1

4.5

142,885,934,392,500

0.002294

0.010322

Flush

Yes

5

1

2.5

48,427,468,492,500

0.000777

0.001944

Straight

Yes

4

1

2

51,929,927,490,000

0.000834

0.001667

Three of a kind

Yes

3

1

1.5

184,235,372,548,500

0.002958

0.004436

Two pair

Yes

2

1

1

266,123,076,963,750

0.004272

0.004272

Jacks or better

Yes

1

1

0.5

417,840,544,995,000

0.006708

0.003354

Royal flush

No

800

1

400

-

0.000000

0.000000

Straight flush

No

55

1

27.5

-

0.000000

0.000000

Four of a kind

No

25

1

12.5

-

0.000000

0.000000

Full house

No

9

1

4.5

-

0.000000

0.000000

Flush

No

5

1

2.5

484,274,684,925,000

0.007774

0.019436

Straight

No

4

1

2

519,299,274,900,000

0.008337

0.016673

Three of a kind

No

3

1

1.5

3,684,707,450,970,000

0.059153

0.088729

Two pair

No

2

1

1

6,653,076,924,093,750

0.106806

0.106806

Jacks or better

No

1

1

0.5

10,446,013,624,875,000

0.167696

0.083848

Loser

No

0

1

0

34,790,044,215,112,500

0.558505

0.000000

Total

62,291,345,366,250,000

1.000000

0.987504

Analysis

This game was pretty easy to analyze. Here is how I did it.

Determine the average multiplier, assuming the Double Up feature was won. It requires simple math to see the probability of a 1x multiplier is (1/5), 2x is (4/5)×(2/5), 4x is (4/5)×(3/5)×(3/5), 8x is (4/5)×(3/5)×(2/5)×(4/5), and 16x is (4/5)×(3/5)×(2/5)×(1/5). The following table shows the probability of each multiplier. The lower right cell shows the average multiplier earned is 3.8352.

Multiplier Table

Multiplier

Combinations

Probability

ExpectedMultiplier

1

125

0.2000

0.2000

2

200

0.3200

0.6400

4

180

0.2880

1.1520

8

96

0.1536

1.2288

16

24

0.0384

0.6144

Total

625

1.0000

3.8352

Determine the "adjusted pay" for each hand. This is how much the player can expect to win, on average, for each hand on the draw, relative to his total wager. This is defined as w*(p*3.8352 + (1-p)*1)/2 = w*(p*2.8352 + 1)/2, where w = base win for the hand and p=probability of bonus feature. The reason for dividing by 2 is the player must double his bet to enable the Double Up feature.

For example, in 9-5 Jacks or Better the base win for a flush is 5, and the probability of the feature is 1/3. So the expected final win for a flush is 5×((1/3)×2.8352 + 1)/2 = 4.8627.

Use my video poker return analyzer, putting the adjusted pays in the prize column. Note that the calculator doesn't accept decimals in that column. What I did was multiply the adjusted awards by 100 and rounded that product to the nearest integer.

Use the resulting combinations to get the probability of each hand and create a return table.

If you encounter a pay table not on this page for this game you can use this method to find the return yourself. This method of calculating the adjusted win can also be used to create strategies for any game using my video poker strategy calculator.